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Global-in-time solutions and Hölder continuity for quasilinear parabolic PDEs with mixed boundary conditions in the Bessel dual scale
We proved the existence and uniqueness of global-in-time solutions in the $ W^{-1,p}_D $-$ W^{1,p}_D $ setting for abstract quasilinear parabolic PDEs with nonsmooth data and mixed boundary conditions, including a nonlinear source term with at most linear growth. Subsequently, we used a bootstrapping argument to achieve improved regularity, in …